Ion Implantation and Synthesis of Materials - Studium

4 Cross-Section4.1 IntroductionIn Chap. 3 we derived equations describing the kinematics of binary elastic collisions.These equations enable us to calculate the amount of energy-transferred to atarget atom in a collision when the scattering angle of the projectile or the targetatom is known. Conversely, we could calculate the scattering angle if the amountof energy loss in the collision was known.In Chap. 4 we will examine the probability of ion–solid scattering events. Duringion irradiation and ion implantation experiments, many ions or energetic particlesinteract with many target nuclei. Due to the large number of interactions, thequestions of how much energy will be transferred in a collision or what the scatteringangle will be must be answered using statistics and probability. The differentialcross-section is the fundamental parameter that we will develop. It gives ameasure of either the probability of transferring energy T in the range between Tand T + dT to a target atom, or of the probability of scattering a projectile intosome angle between θ c and θ c + dθ c . The differential cross-section has units ofarea, typically centimeters squared. The differential cross-section integrated overall angles is the total cross-section, often referred to simply as the cross-section.The differential cross-section will become an important parameter in describingion ranges in solids and radiation damage, both of which will be discussed later inthis book. The differential cross-section depends strongly on the form of the interatomicpotential.4.2 Scattering Cross-SectionIn ion–solid interactions, it is customary to describe the number of particles scatteredthrough different angles, θ c , in terms of a quantity called the angular differentialscattering cross-section. Imagine the experiment depicted in Fig. 4.1, wherea beam of ions is incident on a thin foil and is scattered into a detector of area ∆aat a polar angle between θ c and θ c + dθ c . Each of the ions in the incident37